The Israeli military launched a ground operation into Gaza late Thursday and called an extra 18,000 reservists into the conflict with Hamas.
Prime Minister Benjamin Netanyahu and Defense Minister Moshe Yaalon ordered the ground action to destroy tunnels from Gaza into Israeli territory, according to a statement from Netanyahu's media adviser.
Thirteen Hamas militants used a tunnel earlier Thursday to launch an attempted attack in Sufa, near an Israeli kibbutz, but were stopped by Israeli soldiers, the Israel Defense Forces reported.
CNN's Wolf Blitzer asked Mark Regev, Netanyahu's spokesman, whether Israel planned to occupy Gaza for a long time.
Regev didn't answer directly, but said Israel's goals are to "diminish" the Hamas military force and to show Hamas it cannot attack Israel with impunity.
"We have hit Hamas hard, and we will continue to hit Hamas hard," the Israel Defense Forces tweeted.
Hamas immediately condemned the Israeli operation.
Hamas spokesman Fawzi Barhoum told CNN that "the beginning of the Israeli ground invasion of Gaza is a dangerous step with unknown consequences. Israel will pay a heavy price for it."
Later, appearing on Aqsa TV, Barhoum said, "the resistance will confront the Israeli ground invasion and will defend the people of Gaza."
He said Hamas military forces are "far stronger" than in 2009 and 2012, when Hamas and Israel clashed.
Militants are prepared to capture Israel soldiers and use them to trade for some of 5,000 prisoners in Israeli jails, Barhoum said.
CNN's Palestinian security sources said Israeli tanks have reached Abu Holeh and that Israeli troops are clashing with Hamas and Islamic Jihad fighters along the Kissufim road.
Abu Holeh is about in the center of Gaza, said CNN reporter Ben Wedeman. If Israeli forces go from there to the sea they can split Gaza as they did during the 2009 ground operation, Wedeman said.
Wedeman said Israeli forces struck near a mosque in Gaza City's Zaitoun neighborhood, which has been pounded since start of bombing, with many casualties reported.
Gaza hospital struck
Kenneth Roth, executive director of Human Rights Watch, said Israeli bombs hit Wafa Hospital in Gaza while four patients were inside. Seventeen others had evacuated, he said.
The long-awaited ground operation follows one of the worst nights of fighting since the war began. That fighting began after a temporary cease-fire ended earlier in the day.
The Gaza Health Ministry said seven children were killed in three hours on Thursday.
Before the incursion, the IDF dropped leaflets in 14 areas of Gaza, urging residents to temporarily leave their homes.
CNN reporter Ian Lee described the action: "Periodic fire balls illuminate the sky over Gaza. We see rockets screech toward the sky. Minutes later we see an intercepting missile rise from the iron dome, reducing the rocket into confetti of light and fire.
"We've seen red tracer rounds fly across the horizon. The repetitive thud of naval guns echoes throughout the coastal strip."
A 4-year-old girl was killed in an Israeli airstrike near the customs building in Khan Younis, Palestinian medical and security sources said, and another airstrike killed a 29-year-old man east of Khan Younis.
Aqsa TV reported that an Israeli was killed and another injured in shelling of Ashkelon and that seven Israeli soldiers were injured in an attack on a military location.
Aqsa TV also reported that Israeli gunboats near Beit Lahiya north of Gaza strip, fired at the homes of residents.
Palestinian medical and security sources say 246 people have been killed in Gaza and more than 1,850 injured. Israel says one of its citizens has died.